I feel like deportation or maximal Confederate exodus would likely work best if there were a fairly nearby and distinct place of exile to make it work- perhaps a French backed trans-Mississippi or Texas, or Florida rump-CSA, or a prewar established filibuster state in Mexico (Baja or Sonora, or maybe, for an alternate twist- a republic of Rio Grande) or Nicaragua that gets set up and somehow survives through the war. The trick is that a USA able to reconquer the main body of any CSA, should also be able to re-conquer any of its peripheries. The Union may lack a similar commitment to conquering/absorbing a filibuster state in Mexico or Central America that had never been accepted into the Union. Odds would still be it would want the filibuster regime overthrown or restored to republican Mexico or native rule, but if that doesn't happen, filibuster-land could be a convenient dumping ground for irreconcilable Rebs.
I don't know quite how you could go about applying it to the American context, but the Syrian civil war of the 21st century has seen an interesting on-again/off-again, stop-/start pattern where the central government retakes rebel held areas bite by bite. It does so harshly, but it has several times allowed enemy fighters, leaders and supporting populations safe passage to fleet to remaining rebel held areas, as a pragmatic method to hold down the casualties the government would incur by taking the territory by storm from trapped rebels. In this way, the regime has "corralled" rebels into fewer and fewer areas, rebels have survived to live/fight another day, and the regime has had an easier, cleaner way to control reoccupied territory.
Of course the 21st century Syrian civil war is much more internationalized, with Syria being a weaker state, relying on foreign patronage. I lack the creativity/imagination to impose a similar process on the United States Civil War.